In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?

The length of Diagonal is 14.73 unit.

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Given:

l = 9, w= 10 and h= 6

The Formula for Diagonal length of Prism is:

d =√l² + w² + h²

Here, d = length of the diagonal, l = length of the rectangular base of the prism, w = width of the rectangular base of the prism, and h = height of the prism.

Substitute the value in the equation,

d =√9² + 10² + 6²

d =√81+ 100 + 36

d = √217

d =  14.73 units

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As per the given angle the value of x makes MRNW a kite is 6.66 degrees

Now, let's use the information given to us to find the value of x that makes MRNW a kite. We know that the angle ∠RMN is 5x - 15, and we know that the angle ∠R is 11x + 45. Since MR and RN are equal in length, we know that ∠RMN and ∠R are adjacent angles in a straight line. This means that their sum is equal to 180 degrees.

So, we can write an equation:

(5x - 15) + (11x + 45) = 180

Simplifying this equation, we get:

16x + 30 = 180

Subtracting 30 from both sides, we get:

16x = 150

Dividing both sides by 16, we get:

x = 9.375

To do this, we need to find the values of the other two angles in the kite. We know that the angle ∠WNM is 10y + 30, and we know that the angle ∠W is 8y.

So, we can write another equation:

(10y + 30) + (8y) = 180

Simplifying this equation, we get:

18y + 30 = 180

Subtracting 30 from both sides, we get:

18y = 150

Dividing both sides by 18, we get:

y = 8.333

Now, we need to check if these values of x and y make MRNW a kite. We can calculate the angles ∠M and ∠N using the information we have:

∠M = 180 - ∠RMN - ∠R

∠M = 180 - (5x - 15) - (11x + 45)

∠M = 150 - 16x

∠M = 7.5 degrees

∠N = 180 - ∠WNM - ∠W

∠N = 180 - (10y + 30) - (8y)

∠N = 142 - 18y

∠N = 6.666 degrees

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Complete Question;

Use the given figure to answer questions 4-6. MRNW is a kite. ∠RMN = 5x - 15, ∠R = 11x + 45, ∠WNM = 10y + 30, and ∠W = 8y. 4. What value of x makes MRNW a kite?

Answer:

m = -3/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, − 6) and (− 2, 3)

We see the y increase by 9 and the x decrease by 6, so the slope is

m = - 9/6 = -3/2

So, the slope of the line is -3/2

The number that was excluded from the 10 consecutive numbers would be = 228.

Let's take the smallest number of the 10 consecutive number to be = X

Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)

Collect the like terms and add up.

= 9x + 36

Recall that the sum of the remaining 9 numbers = 2023.

That is:

= 9X + 36 = 2023

=9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

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Answer: 54 cups of sugar

Step-by-step explanation:

part A  add 3 each time

1=3

2=6

3=9

4=12

5=15

6=18

Part B

1x3 per pie

so if there is 70 pies do 70x3

Part C]

if you do 18 and since you need 3 cups of sugar per pie

do 18 times 3 to get a total of 54 cups of sugar

18x3=54

The given exponential functions are classified as exponential growth or exponential decay above.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to check whether the given functions represent exponential growth or decay.

We can write the classified functions as -

{ 1 }.   y = 500(0.30)ˣ                     exponential decay

{ 2 }.  y = 500(1.70)ˣ                      exponential growth

{ 3 }.  y = 0.3(500)ˣ                       exponential growth

{ 4 }.  y = 500(0.30)ˣ - 6               exponential decay

{ 5 }.  y = 0.3(1.7)ˣ - 2                    exponential growth

{ 6 }.  y = 500(0.30)ˣ ⁺ ⁸               exponential growth

{ 4 }.  y = 500(0.30)ˣ ⁻ ⁶               exponential decay

Therefore, the given exponential functions are classified as exponential growth or exponential decay above.

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Assuming a constant rate of production, 360 workers can produce approximately 7200 widgets in 20 hours.

The problem asks how many widgets can be produced by 360 workers in 20 hours. To solve this problem, we need to use the formula:

widgets = rate x time x workers

We know the time is 20 hours and the number of workers is 360. We need to find the rate at which the workers can produce widgets. Let's assume that each worker can produce one widget in one hour, so the rate is 1 widget per worker-hour.

Substituting the values, we get:

widgets = 1 x 20 x 360

widgets = 7200

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Answer: 18

Step-by-step explanation:

9 kids each have two bags

9 x 2 = 18

9 + 9 = 18

The weight of the baby elephant is less than 212.59 kilograms which can be calculated using inequality.

To solve this problem, we need to use the inequality and the given information to find the weight of the baby elephant and the adult elephant. We can write the inequality as follows:

27w + 400 < a

Where w is the weight of the baby elephant in kilograms, and a is the weight of the adult elephant in kilograms. We can rearrange this inequality to get:

w < (a - 400)/27

Now, we can plug in the given information to find the weight of the baby elephant and the adult elephant. For example, if the weight of the adult elephant is 6000 kilograms, we can plug this into the inequality and get:

w < (6000 - 400)/27

w < 212.59

Similarly, we can plug in different values for the weight of the adult elephant to find the weight of the baby elephant.

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Answer:

410=50x+10

Step-by-step explanation:

your total is 410 so to get there you have to know the number of nights which is x. the 10 is a one time fee so you only need that once and not per night.

Answer:

6x-4y=18

-x-6y=7

-x-6y=7

-x=7+6y

x=-7-6y

6x-4y=18

6(x-7-6y)-4y=18

-42-40y=18

-40y=18+42

-40y=60

y=-60/40

y=-3/2

x=-7-6y

x=-7-6(-3/2)

x=-7+9

x=2

(x,y) = (2,-3/2)

The mean of the list  is 7

The standard deviation of the list is 4/69

The linear regression equation is y = 227.5 + 0.65*x
The percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.

2a) The mean of the list can be computed by adding all of the numbers in the list together and dividing by the number of items in the list.

Mean = (9+2+5+4+12+10)/6 = 42/6 = 7

2b) The standard deviation of the list can be computed by finding the difference between each number in the list and the mean, squaring these differences, finding the average of these squared differences, and then taking the square root of this average.

Standard deviation = sqrt(((9-7)^2 + (2-7)^2 + (5-7)^2 + (4-7)^2 + (12-7)^2 + (10-7)^2)/6) = sqrt(22) = 4.69

3a) The linear regression equation can be found using the formula:

y = b0 + b1*x

Where b0 is the y-intercept and b1 is the slope. The slope can be found using the formula:

b1 = r*(SDy/SDx)

Plugging in the given values:

b1 = 0.80*(85/105) = 0.65

The y-intercept can be found using the formula:

b0 = meany - b1*meanx

Plugging in the given values:

b0 = 570 - 0.65*525 = 227.5

So the linear regression equation is:

y = 227.5 + 0.65*x

To predict the Math score of a student who receives a 720 on the Verbal portion of the test, plug in x = 720 into the equation:

y = 227.5 + 0.65*720 = 693

So the predicted Math score is 693.

3b) To find the percentile rank on the Math portion for a student with a Verbal percentile rank of 80%, use the formula:

z = (x-mean)/SD

Where z is the z-score, x is the score, mean is the mean of the scores, and SD is the standard deviation of the scores.

Plugging in the given values for the Verbal scores:

z = (x-525)/105

Solving for x:

x = 105*z + 525

Since the Verbal percentile rank is 80%, the z-score is 0.84 (from a z-table). Plugging this into the equation:

x = 105*0.84 + 525 = 613.2

So the Verbal score corresponding to the 80th percentile is 613.2.

To find the Math score corresponding to this Verbal score, plug in x = 613.2 into the linear regression equation:

y = 227.5 + 0.65*613.2 = 623.6

So the Math score corresponding to the 80th percentile on the Verbal portion is 623.6.

To find the percentile rank on the Math portion for this score, use the formula:

z = (x-mean)/SD

Plugging in the given values for the Math scores:

z = (623.6-570)/85 = 0.63

Using a z-table, the corresponding percentile rank is approximately 73.5%.

So the percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.

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The expression (18)(-3)(-3) is not equivalent to others.

-7+(-3) is equivalent of the expression -7 - 3.

What is an expression?

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical value is referred to as a constant.

Variable: A symbol without a fixed value is referred to as a variable.

Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.

Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Take the first option:

(-9)(-3 × -6)

= (-9)(18)

= (18)(-9)  [Commutative property]

= -(-18)(-9)

Apply the associative property on (-9)(-3 × -6):

(-9)(-3 × -6)

= (-9× - 3)(-6)

= (27) (-6)

= (-6)(27)   [Commutative property]

The given expression is -7 - 3

Rewrite the above expression:

-7+(-3)

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Answer:

3) The commercial costs $900 to produce and $110 each times it is aired.

Step-by-step explanation:

We can determine how expensive it is to produce a commercial by looking at the function C(n)'s output when n = 0 (when the commercial hasn't been aired yet).

C(0) = 110(0) + 900

C(0) = $900

So, the cost of producing a commercial is $900.

We can see that $110 is added to the cost each time n is incremented by 1. Therefore, it costs $110 each time the commercial is aired.

We can put these two statements together to deduce that answer option 3 is correct:

The commercial costs $900 to produce and $110 each times it is aired.

Answer:

Option 3

Step-by-step explanation:

900 is a constant number that never changes. However, the value of "110n" changes every time it is aired, because 110 is multiplied by a different number. This means that $110 represents the cost of airing it each time, because if it was hypothetically aired three times, you would multiply 110 by 3, proving that it is the cost to air it, and $900 is the production cost. It also makes no sense to produce the same commercial over and over again, so the cost that is multiplied has to be the amount of times that it is aired.

The value of a when b=4 and c=4 is 72.70. Rounded to two decimal places, the answer is 72.70.

The variable a is jointly proportional to the cube of b and the square of c. This means that the relationship between a, b, and c can be expressed as: a = k * b^3 * c^2, where k is a constant of proportionality.

When a=433, b=5, and c=7, we can plug these values into the equation to find the value of k:
433 = k * 5^3 * 7^2
433 = k * 125 * 49
433 = k * 6125
k = 433/6125
k = 0.07069

Now, we can use this value of k to find the value of a when b=4 and c=4:
a = k * b^3 * c^2
a = 0.07069 * 4^3 * 4^2
a = 0.07069 * 64 * 16
a = 72.70

Therefore, the value of a when b=4 and c=4 is 72.70. Rounded to two decimal places is 72.70.

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The measures of the other three angles are: ∠2 = ∠3 = 67.5° and ∠4 = 0°.

An angle is a geometric figure formed by two rays that share the same endpoint called vertex. It is measured in degrees, radians or gradians and is usually denoted by the vertex letter in its center, with the endpoints labeled by two other letters or points.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can use this information to find the measures of the other three angles.

If ∠1 has a measure of 45°, then we know that the sum of the measures of ∠2 and ∠3 is 135° (180° - 45°).

If the triangle is isosceles, then ∠2 and ∠3 have the same measure. Therefore, we can divide 135° by 2 to get:

∠2 = ∠3 = 67.5°

Finally, we can use the fact that the angles of a triangle add up to 180° to find the measure of ∠4:

∠4 = 180° - 45° - 67.5° - 67.5° = 0°

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The given polynomial g(x) is g(x)=x^(3)+(p-4)x^(2)+(p-9)x-4.

To show that the polynomial g(x) is divisible by (x+1) for all values of p, we must prove that g(x) has a factor of (x+1). This can be done by expanding the given polynomial and rewriting it in a form that contains the factor (x+1).

First, we expand the given polynomial g(x):

g(x)=(x^3 + (p-4)x^2 + (p-9)x - 4)

= x^3 + px^2 - 4x^2 + px - 9x - 4

= x^3 + (p-4)x^2 + (px - 9x) - 4

= x^3 + (p-4)x^2 + (p - 9)x - 4

Now we can factor out the term (x+1) from the expression:

= (x^3 + (p-4)x^2 + (p-9)x - 4)

= (x+1)(x^2 + (p-5)x + (p-9)) - 4

Finally, we can rewrite the expression as:

g(x)=(x+1)(x^2 + (p-5)x + (p-9)) - 4

This shows that the polynomial g(x) is divisible by (x+1) for all values of p, as there is a factor of (x+1) in the expression.

Therefore, we have successfully proved that the polynomial g(x) is divisible by (x+1) for all values of p.

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A single point perspective projection onto the z=0 plane from a center of projection at z=-2 are A' = (3/4, 2/4, 0) = (0.75, 0.5, 0) for point A and B' = (3/8, 2/8, 0) = (0.375, 0.25, 0) for point B. There are no vanishing points at infinity along the x, y, and z-axis for this case.

To perform a single point perspective projection onto the z=0 plane from a center of projection at z=-2, we need to use the perspective projection formula:

P' = (x/z, y/z, 0)

For point A(3, 2, 4, 1), the projected point A' will be:

A' = (3/4, 2/4, 0) = (0.75, 0.5, 0)

For point B(3, 2, 8, 1), the projected point B' will be:

B' = (3/8, 2/8, 0) = (0.375, 0.25, 0)

Now, to determine the vanishing points at infinity along the x, y, and z-axis, we need to find the points where the line segment AB intersects the planes at infinity along each axis.

For the x-axis, the plane at infinity is x=∞. Since the line segment AB is parallel to the x-axis, it will never intersect this plane, and therefore there is no vanishing point along the x-axis.

For the y-axis, the plane at infinity is y=∞. Similarly, the line segment AB is parallel to the y-axis and will never intersect this plane, so there is no vanishing point along the y-axis.

For the z-axis, the plane at infinity is z=∞. The line segment AB is not parallel to the z-axis, so it will intersect this plane at a point with coordinates (x, y, ∞). To find this point, we can use the equation of the line segment AB:

(x - 3)/(3 - 3) = (y - 2)/(2 - 2) = (z - 4)/(8 - 4)

Solving for z=∞, we get:

(x - 3)/(3 - 3) = (y - 2)/(2 - 2) = (∞ - 4)/(8 - 4) = ∞

Since the denominators are all equal to zero, this equation is undefined, and therefore there is no vanishing point along the z-axis.

In conclusion, there are no vanishing points at infinity along the x, y, and z-axis for this case.

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Answer: The other game companies offer

Step-by-step explanation: Pretty much self-explanatory.

Check the picture below.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0}\implies \cfrac{18-12}{2}\implies \cfrac{6}{2}\implies \text{\LARGE 3}[/tex]

Answer:

To divide £300 in the ratio of 10:20, we need to first add the two parts of the ratio to find the total number of parts:

10 + 20 = 30

This means that the ratio can be expressed as 10/30 and 20/30.

Next, we can use these ratios to find the amount of money for each part of the ratio:

10/30 x £300 = £100

20/30 x £300 = £200

Therefore, the amount of money for the parts of the ratio 10:20 would be £100 and £200 respectively.

The values of the variables are y =50 and x = 130

From the question, we have the following parameters that can be used in our computation:

The isosceles trapezoid

An isosceles trapezoid is a quadrilateral with two parallel sides of equal length and two non-parallel sides of unequal length.

This means that the base angles are congruent

Using the above as a guide, we have the following for the variable y

y = 50

Solving further, we have the following equation for variable x

x + 50 = 180

Evaluate the equation

x = 130

Hence, the value of x is 130

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The solution to the system of equations is:
x = -6.552
y = -1.655
z = 1.276

To solve the system of equations using the inverse of the coefficient matrix, we will first need to find the inverse of the coefficient matrix using the inversion algorithm. The coefficient matrix is:

A = [[2, 6, 6], [2, 7, 1], [2, 7, 7]]

To find the inverse of A, we will use the inversion algorithm:

1. Find the determinant of A:

|A| = 2(7*7 - 1*7) - 6(2*7 - 1*2) + 6(2*7 - 2*7) = 14 - 72 + 0 = -58

2. Find the matrix of minors:

M = [[(7*7 - 1*7), -(2*7 - 1*2), (2*7 - 2*7)], [-(6*7 - 6*1), (2*7 - 6*2), -(2*6 - 6*2)], [(6*1 - 7*6), -(2*1 - 7*2), (2*6 - 7*6)]]

M = [[42, -12, 0], [-36, 2, -12], [-36, 12, -30]]

3. Find the matrix of cofactors:

C = [[42, 12, 0], [36, 2, 12], [-36, -12, -30]]

4. Find the adjugate matrix:

adj(A) = [[42, 36, -36], [12, 2, -12], [0, 12, -30]]

5. Find the inverse of A:

A^-1 = (1/|A|)adj(A) = (1/-58)[[42, 36, -36], [12, 2, -12], [0, 12, -30]]

A^-1 = [[-0.724, -0.621, 0.621], [-0.207, -0.034, 0.207], [0, -0.207, 0.517]]

Now, we can use the inverse of the coefficient matrix to solve the system of equations. The system of equations can be written in matrix form as:

AX = B

Where A is the coefficient matrix, X is the matrix of unknowns, and B is the matrix of constants:

A = [[2, 6, 6], [2, 7, 1], [2, 7, 7]]
X = [[x], [y], [z]]
B = [[6], [7], [8]]

Multiplying both sides of the equation by the inverse of A, we get:

A^-1AX = A^-1B

IX = A^-1B

X = A^-1B

Substituting the values of A^-1 and B, we get:

X = [[-0.724, -0.621, 0.621], [-0.207, -0.034, 0.207], [0, -0.207, 0.517]] * [[6], [7], [8]]

X = [[-6.552], [-1.655], [1.276]]

Therefore, the solution to the system of equations is:

x = -6.552
y = -1.655
z = 1.276

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A. Amplitude: 4,  Asymptotes: None,  Complete Period:  [tex]\(\frac{2\pi}{5}\)[/tex],  Period: [tex]\(2\pi/5\)[/tex],  Phase Shift:  [tex]\(\frac{\pi}{5}\)[/tex].
B. Amplitude: 1, Asymptotes:  [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex], Complete Period:  [tex]\frac{2\pi}{3}\)[/tex],     Period:  [tex]\(2\pi/3\)[/tex],  Phase Shift: [tex]\(\frac{\pi}{6}\)[/tex].

To find the amplitude, asymptotes, complete period, period, and phase shift for each of the given trigonometric functions, we need to use the standard form of the trigonometric functions:[tex]\[f(x)=A\sin(Bx+C)+D\][/tex] and [tex]\[g(x)=A\sec(Bx+C)+D\][/tex]

For function f(x), we have:
A = 4, B = 5, C = -π, and D = 0

The amplitude is |A| = |4| = 4

The period is  [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{5}\)[/tex]

The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi}{5}[/tex] = [tex]\frac{\pi}{5}\)[/tex]

There are no asymptotes for the sine function.

For function g(x), we have:
A = -1, B = 3, C = -π/2, and D = 0

The amplitude is |A| = |-1| = 1

The period is [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{3}\)[/tex]

The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi/2}{3}[/tex] = [tex]\frac{\pi}{6}\)[/tex]

The asymptotes occur when the cosine function is equal to zero, so the asymptotes are at  [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex] , where n is an integer.

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The number of copies sold in total is 586,301

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, a book sold 42800 copies in its first month of release, this represents 7.3 of the number of copies sold to date, we need to find the number of the copies have been sold to date,

Let the number of copies sold in total be x,

Using the concept of percentage,

7.3 % of x = 42800

7.3 / 100 of x = 42800

x = 100/7.3 (42800)

x = 586,301

Hence, the number of copies sold in total is 586,301

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The solutions of the equation  0=x^2-9x+8 are x = 8 and x = 1

From the question, we have the following parameters that can be used in our computation:

0=x^2-9x+8

Rewrite as

x^2 - 9x + 8 = 0

Expand the equation

So, we have the following representation

x^2 - 8x - x + 8 = 0

When the equation is factorized, we have

(x - 8)(x - 1) = 0

This gives

x - 8 = 0 and x - 1 = 0

Evaluate

x = 8 and x = 1

Hence, the solutions are x = 8 and x = 1

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Answer:

I need a graph to answer this question

Step-by-step explanation:

For function fx= -4x2+6x-1

To find f(-1), we need to plug in -1 for x in the function and simplify:
f(-1) = -4(-1)2+6(-1)-1
f(-1) = -4+(-6)-1
f(-1) = -11

To find when fx=0, we need to set the function equal to 0 and solve for x: -4x2+6x-1=0

We can use the quadratic formula to solve for x:
x = (-b ± √(b2-4ac))/(2a)
x = (-(6) ± √((6)2-4(-4)(-1)))/(2(-4))
x = (-6 ± √(36-16))/(-8)
x = (-6 ± √20)/(-8)
x = (-6 ± 2√5)/(-8)
x = (3 ± √5)/4

So, the two values of x that make fx=0 are (3+√5)/4 and (3-√5)/4.

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(a) We can use the identity cos(180° - θ) = -cos(θ) to rewrite cos(165°) as cos(180° - 15°) cos(165°) = cos(180° - 15°) = -cos(15°) To find cos(15°),

we can use the half-angle formula for cosine: cos(15°) = cos(30°/2) = sqrt((1 + cos(30°))/2) = sqrt((1 + sqrt(3)/2)/2) = (sqrt(2) + sqrt(6))/4

Therefore, cos(165°) = -cos(15°) = -(sqrt(2) + sqrt(6))/4 (b) Using the product-to-sum identity, we have cos(80°)cos(20°) + sin(80°)sin(20°) = cos(80° - 20°) = cos(60°) = 1/2 Therefore, cos(80°)cos(20°) + sin(80°)sin(20°) = 1/2.

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Answer:

x = 106 degrees

Step-by-step explanation:

we can create a triangle with angles x, 30, and 26+18.

that means x + 30 + (26 + 18) = 180.

move the constants to one side to get x = 180 - 30 - (26 + 18) = 106